Problem: The grades on a chemistry midterm at Covington are normally distributed with $\mu = 78$ and $\sigma = 5.0$. Gabriela earned a $71$ on the exam. Find the z-score for Gabriela's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Gabriela's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{71 - {78}}{{5.0}}} $ ${ z \approx -1.40}$ The z-score is $-1.40$. In other words, Gabriela's score was $1.40$ standard deviations below the mean.